Non-king elimination, intransitive triad interactions, and species coexistence in ecological competition networks
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ORIGINAL PAPER
Non-king elimination, intransitive triad interactions, and species coexistence in ecological competition networks Nathan Muyinda1,2
· Bernard De Baets2 · Shodhan Rao1,2
Received: 30 January 2020 / Accepted: 26 April 2020 © Springer Nature B.V. 2020
Abstract Ecological communities are characterized by the interactions among the species living within a given habitat and can be conveniently represented as networks of interactions. Variation in the way the interactions are organized in the network determines whether the ecological community is able to support coexistence and resist collapse. Analyzing network properties can thus provide insights as to why some species persist while others go extinct and provide solutions to one of community ecology’s central aim, the prediction of community structure at equilibrium. In this work, we highlight an approach that makes use of the properties of the network to determine the equilibrium species composition and richness in a number of competition networks represented by complete directed graphs (tournaments). We show that in any tournament, all non-kings get eliminated resulting in a smaller tournament in which every species is a king. At this point, the pairwise interactions among species are not sufficient to determine community structure and it is the interactions among the intransitive triads of the tournament that fundamentally determine how many species persist. Keywords Zero-sum game · Community composition · Optimal strategy · Tournament kings · Final species richness · Triad-interaction graph
Introduction Species interactions are one of the central factors determining the structure of ecological communities (Valladares et al. 2015; Ponisio et al. 2019; Ovaskainen et al. 2017). In animals, these interactions often involve direct aggression (interference competition) among species with the dominant species displacing subordinates from shared resources such as food and from the safest and most preferred feeding Nathan Muyinda
[email protected] Bernard De Baets [email protected] Shodhan Rao [email protected] 1
Center for Biotech Data Science, Ghent University Global Campus, 119 Songdomunhwa-Ro, Yeonsu-Gu, Incheon, South Korea
2
KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, 9000 Ghent, Belgium
sites. In many theoretical studies, competitive interactions among pairs of species are assumed to be asymmetric, characterized by a consistent outcome, with one consistently dominant species and one consistently subordinate species (Morse 1974; Drews 1993; Francis et al. 2018; Martin and Bonier 2018). This leads to competition networks that can be represented by complete directed graphs, also known as tournaments, whose nodes are the species and the edges (arrows) point from the competitive subordinate to the competitive dominant (Otto and Day 2007). These networks can take many structural forms ranging from linear hierarchies to intransitive competition networks (Miller et al. 2017;
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